This section briefly overviews the optimization-based problem in truth discovery that we adopt for CPT aggregation. The basic idea is that the inferred truth is likely to be correct if a reliable source provides it. Therefore, the goal is to minimize the overall distance of the aggregated truth to a reliable source [1]}. Based on this principle, the optimization framework is defined as follows:

\(\min _{\mathcal {X}^*,\mathcal {W}} f(\mathcal {X}^*,\mathcal {W})=\sum _{k=1}^{K} {w_k} \sum _{i=1}^{N} \sum _{m=1}^{M} d_m(v_{im}^*,v_{im}^k)\\s.t. \ {\delta (\mathcal {W})=1 , \mathcal {W}\in \mathcal {S}}, \) 
